Length of a Spiral: More Parametric Mystery

[world of math]

Find the length of the spiral from t=0 to t=4.

x=tcos(pi*t)
y=tsin(pi*t)

So far I decided to get dx and dy. So dx=cos(pi*t)+t*pi*sin(pi*t) and dy=sin(pi*t)-t*pi*cos(pi*t). Then I tried to integrate from 0 to 4 the following: sqrt(1+(dy/dx)^2). Then I'm stuck, since that doesn't seem to be the right equation to be integrated...

 

[pka]

\(\displaystyle \L l = \int\limits_0^4 {\sqrt {\left[ {x'(t)} \right]^2 + \left[ {y'(t)} \right]^2 } dt}\)

 

[world of math]

Thanks! I got it figured out!